There are many types of filter. The more popular ones are:
• Butterworth or maximally flat filter;
• Tchebyscheff (also known as Chebishev) filter;
• Cauer (or elliptical) filter for steeper attenuation slopes;
• Bessel or maximally flat group delay filter.

All of these filters have advantages and disadvantages and the one usually chosen is the filter type that suits the designer’s needs best. You should bear in mind that each of these filter types is also available in low pass, high pass, bandpass and stopband configurations.

Specifying filters
The important thing to bear in mind is that although the discussion on filters starts off by describing low pass filters, we will show you later by examples how easy it is to change a low pass filter into a high pass, a bandpass or a bandstop filter.

Figure 5.17(a) shows the transmission characteristics of an ideal low pass filter on a normalised frequency scale, i.e. the frequency variable (f) has been divided by the passband line frequency ( fp). Such an ideal filter cannot, of course, be realised in practice. For a practical filter, tolerance limits have to be imposed and it may be represented pictorially as in Figure 5.17(b).

The frequency spectrum is divided into three parts, first the passband in which the insertion loss (Ap) is to be less than a prescribed maximum loss up to a prescribed minimum frequency ( fp).

The second part is the transition limit of the passband frequency limit fp and a frequency Ws in which the transition band attenuation must be greater than its design attenuation.

The third part is the stopband limit in which the insertion loss or attenuation is to be greater than a prescribed minimum number of decibels.

Hence, the performance requirement can be specified by five parameters:
• the filter impedance Z0
• the passband maximum insertion loss (Ap)
• the passband frequency limit ( fp)
• the stopband minimum attenuation (As)
• the lower stopband frequency limit (OHMs)

Sometimes, manufacturers prefer to specify passband loss in terms of return loss ratio (RLR) or reflection coefficient (r). We provide Table 5.2 to show you the relationship between these parameters. If the values that you require are not in the table, then use the set of formulae we have provided to calculate your own values.

These parameters are inter-related by the following equations, assuming loss-less reactances:

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